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NEGF Method for Design and Simulation Analysis of Nanoscale MOS Devices
Published in Ashish Raman, Deep Shekhar, Naveen Kumar, Sub-Micron Semiconductor Devices, 2022
A system like a molecule that consists of a large number of discrete particles whose energies and physical state constantly change with time needs a large number of variables to describe the system's state. It does this by using microscopic thermodynamics. A macrostate represents the collective behavior of a system, whereas a microstate describes the entire system in terms of physical quantities of discrete particles. The total number of a microstate is a function of energy E, several particles N, and volume V and is denoted by W(N, V, E) [29]. The thermodynamic properties of any given system can be determined by function W(N, V, E). Figure 12.5 shows the energy, particles, and volume exchange of two systems that are brought into contact.
Chemical Thermodynamics and Thermochemistry
Published in Armen S. Casparian, Gergely Sirokman, Ann O. Omollo, Rapid Review of Chemistry for the Life Sciences and Engineering, 2021
Armen S. Casparian, Gergely Sirokman, Ann O. Omollo
As a second component of thermodynamics, entropy is a measure of the statistical disorder or randomness of a system. The universe tends to move toward greater total disorder, and this is expressed in terms of entropy or S. Entropy, unlike enthalpy, can be found explicitly. Entropy specifically is a measure of the number of microstates available to a chemical system. Microstates are individual possible states of the system, where a state is a particular arrangement of positions for particles and a particular distribution of kinetic energy among those particles. This can be calculated as shown in Equation 5.6, where S is the entropy, k is Boltzmann’s constant, and W is the number of available microstates. S=klnW
Fundamentals of biology and thermodynamics
Published in Mohammad E. Khosroshahi, Applications of Biophotonics and Nanobiomaterials in Biomedical Engineering, 2017
The idea was originally suggested and formulated by Ludwig Boltzmann between 1872 to 1875, but later modified by Max Planck in about 1900. To quote Planck, “the logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases”. A macrostate has to involve an amount of matter sufficiently large so that we can measure its volume, pressure and temperature. However, in thermodynamics, this is not strictly true. A macrostate is the thermodynamic state of any system that is exactly characterized by measurement of the system’s properties such as P, V, T, H, and number of moles of each constituent, and a microstate deals with the energy that molecules or other particles have. A microstate deals with the possibility of different accessible arrangements of the molecules’ dynamical energy for a particular macrostate. A macrostate does not change over time if its observable and measurable properties do not change, while a microstate of a system is specifically concerned with time and the energy of molecules in that system. Therefore, a microstate is one of the many distinct ways that the microscopic objects making up our macroscopic system can be arranged. For example, let us suppose we are interested in disposition of a fluorescently labeled molecule on a surface. There are various ways of doing this, as each conformation is a specific microstate, but they all have one feature in common, i.e., the molecule is to be adsorbed on the surface.
History of ‘temperature’: maturation of a measurement concept
Published in Annals of Science, 2020
But in 1877, Boltzmann used probability to explore the fact that the speeds and thus the momenta of molecules vary.142 He determined that the probability that some combination of positions and velocities would produce a macroscopic property such as temperature was equal to a number raised to the power of the entropy. Also, since probability here could be calculated by simply counting the number of ways the macroscopic property could be produced, entropy is equal to the logarithm of the number of microstates that produce some macrostate. Boltzmann did not formulate this discovery as we do now, S = k ln W, or use the discovery to much change his thinking about temperature. He did not, for example, use it in any substantial way in his Lectures on Gas Theory, published twenty years later. His colleagues, too, gave it little attention. Max Planck, for example, did not use it in his Treatise on Thermodynamics in 1897.
The paradigm of complex probability and Ludwig Boltzmann's entropy
Published in Systems Science & Control Engineering, 2018
If all the microstates are equiprobable (a microcanonical ensemble), the statistical thermodynamic entropy reduces to the form, as given by Boltzmann: where Ω is the number of microstates, that is the number of microstates that corresponds to the macroscopic thermodynamic state. Therefore S depends on temperature. If all the messages are equiprobable, the information entropy reduces to the Hartley entropy: where is the cardinality of the message space M.
Effects of total cost of ownership on automobile purchasing decisions
Published in Transportation Letters, 2020
The concept of entropy was introduced in thermodynamics by Rudolf Clausius, where it was used to provide a statement of the second law of thermodynamics. Later, statistical mechanics provided a connection between thermodynamic entropy and the logarithm of the number of microstates in a macrostate of the system. Then, Shannon (1948) used entropy to measure the information and defined the entropy measure using a probability mass function as